So any time a character changes his mind that's a plot hole? We're really reaching now.
There are plenty of plot holes and lots of silliness in virtually all the Trek films. Khan taking advantage of the situation to give Kirk a fate he believes is worse than death for Kirk is not one of them.
A plot hole, or plothole, a play on the word "pothole," is a gap or inconsistency in a storyline that goes against the flow of logic established by the story's plot, or constitutes a blatant omission of relevant information regarding the plot sometimes even contradicting itself. These include such things as unlikely behaviour or actions of characters, illogical or impossible events, events happening for no apparent reason, or statements/events that contradict earlier events in the storyline.
Khan wants revenge. That's entirely consistent throughout the film. When Khan thinks Kirk has accidentally gotten himself into a situation where he can be abandoned and forgotten, where he can get his just deserts, karma, he takes the revenge that fate has given him. Kirk plays it up, practically begging Khan to beam down and kill him, which makes Khan even more adamant that he's simply going to leave Kirk there, to not give Kirk the kind of fate appropriate to a hero, which is either victory of death, but to do to Kirk what he did to Khan's wife, which is to simply leave him.